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<div class="header">
  <div class="summary">
<a href="classEigen_1_1DGMRES-members.html">List of all members</a> &#124;
<a href="#pub-methods">Public Member Functions</a> &#124;
<a href="#pro-methods">Protected Member Functions</a>  </div>
  <div class="headertitle">
<div class="title">Eigen::DGMRES&lt; MatrixType_, Preconditioner_ &gt; Class Template Reference<div class="ingroups"><a class="elRef" href="../group__Sparse__chapter.html">Sparse linear algebra</a> &raquo; <a class="elRef" href="../group__Sparse__Reference.html">Reference</a> &raquo; <a class="el" href="group__IterativeLinearSolvers__Module.html">Iterative Solvers module</a></div></div>  </div>
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<div class="contents">
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template&lt;typename MatrixType_, typename Preconditioner_&gt;<br />
class Eigen::DGMRES&lt; MatrixType_, Preconditioner_ &gt;</h3>

<p>A Restarted <a class="el" href="classEigen_1_1GMRES.html" title="A GMRES solver for sparse square problems.">GMRES</a> with deflation. This class implements a modification of the <a class="el" href="classEigen_1_1GMRES.html" title="A GMRES solver for sparse square problems.">GMRES</a> solver for sparse linear systems. The basis is built with modified Gram-Schmidt. At each restart, a few approximated eigenvectors corresponding to the smallest eigenvalues are used to build a preconditioner for the next cycle. This preconditioner for deflation can be combined with any other preconditioner, the <a class="elRef" href="../classEigen_1_1IncompleteLUT.html">IncompleteLUT</a> for instance. The preconditioner is applied at right of the matrix and the combination is multiplicative. </p>
<dl class="tparams"><dt>Template Parameters</dt><dd>
  <table class="tparams">
    <tr><td class="paramname">MatrixType_</td><td>the type of the sparse matrix A, can be a dense or a sparse matrix. </td></tr>
    <tr><td class="paramname">Preconditioner_</td><td>the type of the preconditioner. Default is <a class="elRef" href="../classEigen_1_1DiagonalPreconditioner.html">DiagonalPreconditioner</a> Typical usage : <div class="fragment"><div class="line">SparseMatrix&lt;double&gt; A;</div>
<div class="line"><a class="codeRef" href="../group__matrixtypedefs.html#ga8554c6170729f01c7572574837ecf618">VectorXd</a> x, b; </div>
<div class="line"><span class="comment">//Fill A and b ...</span></div>
<div class="line">DGMRES&lt;SparseMatrix&lt;double&gt; &gt; solver;</div>
<div class="line">solver.set_restart(30); <span class="comment">// Set restarting value</span></div>
<div class="line">solver.setEigenv(1); <span class="comment">// Set the number of eigenvalues to deflate</span></div>
<div class="line">solver.compute(A);</div>
<div class="line">x = solver.solve(b);</div>
<div class="ttc" id="agroup__matrixtypedefs_html_ga8554c6170729f01c7572574837ecf618"><div class="ttname"><a href="../group__matrixtypedefs.html#ga8554c6170729f01c7572574837ecf618">VectorXd</a></div><div class="ttdeci">Matrix&lt; double, Dynamic, 1 &gt; VectorXd</div></div>
</div><!-- fragment --></td></tr>
  </table>
  </dd>
</dl>
<p><a class="el" href="classEigen_1_1DGMRES.html" title="A Restarted GMRES with deflation. This class implements a modification of the GMRES solver for sparse...">DGMRES</a> can also be used in a matrix-free context, see the following <a class="elRef" href="../group__MatrixfreeSolverExample.html">example </a>.</p>
<p>References : [1] D. NUENTSA WAKAM and F. PACULL, Memory Efficient Hybrid Algebraic Solvers for Linear Systems Arising from Compressible Flows, Computers and Fluids, In Press, <a href="https://doi.org/10.1016/j.compfluid.2012.03.023">https://doi.org/10.1016/j.compfluid.2012.03.023</a> <br  />
 [2] K. Burrage and J. Erhel, On the performance of various adaptive preconditioned <a class="el" href="classEigen_1_1GMRES.html" title="A GMRES solver for sparse square problems.">GMRES</a> strategies, 5(1998), 101-121. [3] J. Erhel, K. Burrage and B. Pohl, Restarted <a class="el" href="classEigen_1_1GMRES.html" title="A GMRES solver for sparse square problems.">GMRES</a> preconditioned by deflation,J. Computational and Applied Mathematics, 69(1996), 303-318. </p>
</div><div id="dynsection-0" onclick="return toggleVisibility(this)" class="dynheader closed" style="cursor:pointer;">
  <img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for Eigen::DGMRES&lt; MatrixType_, Preconditioner_ &gt;:</div>
<div id="dynsection-0-summary" class="dynsummary" style="display:block;">
</div>
<div id="dynsection-0-content" class="dyncontent" style="display:none;">
<div class="center"><img src="classEigen_1_1DGMRES__inherit__graph.png" border="0" usemap="#aEigen_1_1DGMRES_3_01MatrixType___00_01Preconditioner___01_4_inherit__map" alt="Inheritance graph"/></div>
<map name="aEigen_1_1DGMRES_3_01MatrixType___00_01Preconditioner___01_4_inherit__map" id="aEigen_1_1DGMRES_3_01MatrixType___00_01Preconditioner___01_4_inherit__map">
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<area shape="rect" target="_parent" href="../classEigen_1_1IterativeSolverBase.html" title=" " alt="" coords="5,175,304,472"/>
<area shape="rect" target="_parent" href="../classEigen_1_1SparseSolverBase.html" title=" " alt="" coords="69,5,240,127"/>
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</div>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:ab1b05e529615d45f3b8c070edfeb82cc"><td class="memItemLeft" align="right" valign="top"><a class="elRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1DGMRES.html#ab1b05e529615d45f3b8c070edfeb82cc">deflSize</a> ()</td></tr>
<tr class="separator:ab1b05e529615d45f3b8c070edfeb82cc"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a60b9241a708ddfd7eb4ff4950faea18c"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1DGMRES.html#a60b9241a708ddfd7eb4ff4950faea18c">DGMRES</a> ()</td></tr>
<tr class="separator:a60b9241a708ddfd7eb4ff4950faea18c"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a38cf741dbc55f3fa4f1a8e0d16713aab"><td class="memTemplParams" colspan="2">template&lt;typename MatrixDerived &gt; </td></tr>
<tr class="memitem:a38cf741dbc55f3fa4f1a8e0d16713aab"><td class="memTemplItemLeft" align="right" valign="top">&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1DGMRES.html#a38cf741dbc55f3fa4f1a8e0d16713aab">DGMRES</a> (const <a class="elRef" href="../structEigen_1_1EigenBase.html">EigenBase</a>&lt; MatrixDerived &gt; &amp;A)</td></tr>
<tr class="separator:a38cf741dbc55f3fa4f1a8e0d16713aab"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a2bd9a6bfc4530cc6d1c1e3312c731bcc"><td class="memItemLeft" align="right" valign="top"><a class="elRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1DGMRES.html#a2bd9a6bfc4530cc6d1c1e3312c731bcc">restart</a> ()</td></tr>
<tr class="separator:a2bd9a6bfc4530cc6d1c1e3312c731bcc"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9732e699838ca2745486fc355eda36e7"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1DGMRES.html#a9732e699838ca2745486fc355eda36e7">set_restart</a> (const <a class="elRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> <a class="el" href="classEigen_1_1DGMRES.html#a2bd9a6bfc4530cc6d1c1e3312c731bcc">restart</a>)</td></tr>
<tr class="separator:a9732e699838ca2745486fc355eda36e7"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:abc45dbf1b2dc85405047157c753db90e"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1DGMRES.html#abc45dbf1b2dc85405047157c753db90e">setEigenv</a> (const <a class="elRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> neig)</td></tr>
<tr class="separator:abc45dbf1b2dc85405047157c753db90e"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a5fe9096f6b96a387b521a866fe344de1"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1DGMRES.html#a5fe9096f6b96a387b521a866fe344de1">setMaxEigenv</a> (const <a class="elRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> maxNeig)</td></tr>
<tr class="separator:a5fe9096f6b96a387b521a866fe344de1"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pro-methods"></a>
Protected Member Functions</h2></td></tr>
<tr class="memitem:a8a47ed3ddd5ac039f9d368c87287a807"><td class="memTemplParams" colspan="2">template&lt;typename Rhs , typename Dest &gt; </td></tr>
<tr class="memitem:a8a47ed3ddd5ac039f9d368c87287a807"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1DGMRES.html#a8a47ed3ddd5ac039f9d368c87287a807">dgmres</a> (const MatrixType &amp;mat, const Rhs &amp;rhs, Dest &amp;x, const Preconditioner &amp;precond) const</td></tr>
<tr class="memdesc:a8a47ed3ddd5ac039f9d368c87287a807"><td class="mdescLeft">&#160;</td><td class="mdescRight">Perform several cycles of restarted <a class="el" href="classEigen_1_1GMRES.html" title="A GMRES solver for sparse square problems.">GMRES</a> with modified Gram Schmidt,.  <a href="classEigen_1_1DGMRES.html#a8a47ed3ddd5ac039f9d368c87287a807">More...</a><br /></td></tr>
<tr class="separator:a8a47ed3ddd5ac039f9d368c87287a807"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1db4ed4c02a85b9479b67be692ade42f"><td class="memTemplParams" colspan="2">template&lt;typename Dest &gt; </td></tr>
<tr class="memitem:a1db4ed4c02a85b9479b67be692ade42f"><td class="memTemplItemLeft" align="right" valign="top"><a class="elRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a>&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1DGMRES.html#a1db4ed4c02a85b9479b67be692ade42f">dgmresCycle</a> (const MatrixType &amp;mat, const Preconditioner &amp;precond, Dest &amp;x, <a class="elRef" href="../classEigen_1_1Matrix.html">DenseVector</a> &amp;r0, RealScalar &amp;beta, const RealScalar &amp;normRhs, <a class="elRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> &amp;nbIts) const</td></tr>
<tr class="memdesc:a1db4ed4c02a85b9479b67be692ade42f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Perform one restart cycle of <a class="el" href="classEigen_1_1DGMRES.html" title="A Restarted GMRES with deflation. This class implements a modification of the GMRES solver for sparse...">DGMRES</a>.  <a href="classEigen_1_1DGMRES.html#a1db4ed4c02a85b9479b67be692ade42f">More...</a><br /></td></tr>
<tr class="separator:a1db4ed4c02a85b9479b67be692ade42f"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
<a id="a60b9241a708ddfd7eb4ff4950faea18c"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a60b9241a708ddfd7eb4ff4950faea18c">&#9670;&nbsp;</a></span>DGMRES() <span class="overload">[1/2]</span></h2>

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<div class="memtemplate">
template&lt;typename MatrixType_ , typename Preconditioner_ &gt; </div>
<table class="mlabels">
  <tr>
  <td class="mlabels-left">
      <table class="memname">
        <tr>
          <td class="memname"><a class="el" href="classEigen_1_1DGMRES.html">Eigen::DGMRES</a>&lt; MatrixType_, Preconditioner_ &gt;::<a class="el" href="classEigen_1_1DGMRES.html">DGMRES</a> </td>
          <td>(</td>
          <td class="paramname"></td><td>)</td>
          <td></td>
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<p>Default constructor. </p>

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</div>
<a id="a38cf741dbc55f3fa4f1a8e0d16713aab"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a38cf741dbc55f3fa4f1a8e0d16713aab">&#9670;&nbsp;</a></span>DGMRES() <span class="overload">[2/2]</span></h2>

<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;typename MatrixType_ , typename Preconditioner_ &gt; </div>
<div class="memtemplate">
template&lt;typename MatrixDerived &gt; </div>
<table class="mlabels">
  <tr>
  <td class="mlabels-left">
      <table class="memname">
        <tr>
          <td class="memname"><a class="el" href="classEigen_1_1DGMRES.html">Eigen::DGMRES</a>&lt; MatrixType_, Preconditioner_ &gt;::<a class="el" href="classEigen_1_1DGMRES.html">DGMRES</a> </td>
          <td>(</td>
          <td class="paramtype">const <a class="elRef" href="../structEigen_1_1EigenBase.html">EigenBase</a>&lt; MatrixDerived &gt; &amp;&#160;</td>
          <td class="paramname"><em>A</em></td><td>)</td>
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<p>Initialize the solver with matrix <em>A</em> for further <code>Ax=b</code> solving.</p>
<p>This constructor is a shortcut for the default constructor followed by a call to <a class="elRef" href="../classEigen_1_1IterativeSolverBase.html#a7dfa55c55e82d697bde227696a630914">compute()</a>.</p>
<dl class="section warning"><dt>Warning</dt><dd>this class stores a reference to the matrix A as well as some precomputed values that depend on it. Therefore, if <em>A</em> is changed this class becomes invalid. Call <a class="elRef" href="../classEigen_1_1IterativeSolverBase.html#a7dfa55c55e82d697bde227696a630914">compute()</a> to update it with the new matrix A, or modify a copy of A. </dd></dl>

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<h2 class="groupheader">Member Function Documentation</h2>
<a id="ab1b05e529615d45f3b8c070edfeb82cc"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ab1b05e529615d45f3b8c070edfeb82cc">&#9670;&nbsp;</a></span>deflSize()</h2>

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template&lt;typename MatrixType_ , typename Preconditioner_ &gt; </div>
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          <td class="memname"><a class="elRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> <a class="el" href="classEigen_1_1DGMRES.html">Eigen::DGMRES</a>&lt; MatrixType_, Preconditioner_ &gt;::deflSize </td>
          <td>(</td>
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<p>Get the size of the deflation subspace size </p>

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<a id="a8a47ed3ddd5ac039f9d368c87287a807"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a8a47ed3ddd5ac039f9d368c87287a807">&#9670;&nbsp;</a></span>dgmres()</h2>

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template&lt;typename MatrixType_ , typename Preconditioner_ &gt; </div>
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template&lt;typename Rhs , typename Dest &gt; </div>
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          <td class="memname">void <a class="el" href="classEigen_1_1DGMRES.html">Eigen::DGMRES</a>&lt; MatrixType_, Preconditioner_ &gt;::dgmres </td>
          <td>(</td>
          <td class="paramtype">const MatrixType &amp;&#160;</td>
          <td class="paramname"><em>mat</em>, </td>
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          <td class="paramtype">Dest &amp;&#160;</td>
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<p>Perform several cycles of restarted <a class="el" href="classEigen_1_1GMRES.html" title="A GMRES solver for sparse square problems.">GMRES</a> with modified Gram Schmidt,. </p>
<p>A right preconditioner is used combined with deflation. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a1db4ed4c02a85b9479b67be692ade42f">&#9670;&nbsp;</a></span>dgmresCycle()</h2>

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template&lt;typename MatrixType_ , typename Preconditioner_ &gt; </div>
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          <td class="memname"><a class="elRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> <a class="el" href="classEigen_1_1DGMRES.html">Eigen::DGMRES</a>&lt; MatrixType_, Preconditioner_ &gt;::dgmresCycle </td>
          <td>(</td>
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<p>Perform one restart cycle of <a class="el" href="classEigen_1_1DGMRES.html" title="A Restarted GMRES with deflation. This class implements a modification of the GMRES solver for sparse...">DGMRES</a>. </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">mat</td><td>The coefficient matrix </td></tr>
    <tr><td class="paramname">precond</td><td>The preconditioner </td></tr>
    <tr><td class="paramname">x</td><td>the new approximated solution </td></tr>
    <tr><td class="paramname">r0</td><td>The initial residual vector </td></tr>
    <tr><td class="paramname">beta</td><td>The norm of the residual computed so far </td></tr>
    <tr><td class="paramname">normRhs</td><td>The norm of the right hand side vector </td></tr>
    <tr><td class="paramname">nbIts</td><td>The number of iterations </td></tr>
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<h2 class="memtitle"><span class="permalink"><a href="#a2bd9a6bfc4530cc6d1c1e3312c731bcc">&#9670;&nbsp;</a></span>restart()</h2>

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<p>Get the restart value </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a9732e699838ca2745486fc355eda36e7">&#9670;&nbsp;</a></span>set_restart()</h2>

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          <td>(</td>
          <td class="paramtype">const <a class="elRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a>&#160;</td>
          <td class="paramname"><em>restart</em></td><td>)</td>
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<p>Set the restart value (default is 30) <br  />
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<h2 class="memtitle"><span class="permalink"><a href="#abc45dbf1b2dc85405047157c753db90e">&#9670;&nbsp;</a></span>setEigenv()</h2>

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          <td class="paramtype">const <a class="elRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a>&#160;</td>
          <td class="paramname"><em>neig</em></td><td>)</td>
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<p>Set the number of eigenvalues to deflate at each restart </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a5fe9096f6b96a387b521a866fe344de1">&#9670;&nbsp;</a></span>setMaxEigenv()</h2>

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template&lt;typename MatrixType_ , typename Preconditioner_ &gt; </div>
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          <td>(</td>
          <td class="paramtype">const <a class="elRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a>&#160;</td>
          <td class="paramname"><em>maxNeig</em></td><td>)</td>
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<p>Set the maximum size of the deflation subspace </p>

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<hr/>The documentation for this class was generated from the following file:<ul>
<li><a class="el" href="DGMRES_8h_source.html">DGMRES.h</a></li>
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